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地铁体育馆站1#出入口基坑支护设计【毕业设计论文计算说明书CAD图纸平面】,毕业设计论文计算说明书CAD图纸平面,地铁,体育馆,出入口,基坑,支护,设计,毕业设计,论文,计算,说明书,CAD,图纸,平面
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毕 业 设 计（论 文）任 务 书1本毕业设计（论文）课题应达到的目的： 基坑支护是为保证基坑开挖、基础施工的顺利进行及基坑周边环境的安全，对基坑侧壁以及周边环境采用的支挡，加固与保护措施。基坑支护体系是临时结构，安全储备较小，具有较大风险，不同水文、工程地质环境条件下基坑工程的差异很大。基坑开挖不仅要保证基坑本身的安全稳定，而且要有效的控制基坑变形以及保护周围环境。 通过该设计，可以培养学生综合运用所学基础理论和专业知识，解决工程实际问题的能力。同时培养学生查阅技术资料，计算机编写设计文件及绘图等综合能力。 2本毕业设计（论文）课题任务的内容和要求（包括原始数据、技术要求、工作要求等）： 1、课题内容和要求南宁市地铁2号线体育馆站位于星光大道与云举路交汇处，沿星光大道敷设。其中1号出入口位于车站的东南角，由1a、1b两个出入口组成，基坑开挖面积约3600m2,开挖深度为12.60m，需垂直开挖。场地处于邕江级阶地。利用所提供的资料对该建筑深基坑支护结构进行设计。 2、设计资料 （1）环境条件拟建场地站位东侧主要建筑为：广西壮族自治区体育局建筑，高6层， a号出入口距建筑物边缘最近处6.0m；泰富大厦，高13层，b号出入口距既有建筑边缘最近处7.0m。星光大道交通繁忙，地下管线较多。（2）岩土层分布及分布特征根据工程勘察报告，影响基坑支护范围内的各土层自上而下为：素填土2（Q4ml）：灰色褐黄色，稍湿湿，松散稍密状态，主要成份为粘性土，夹少量碎石、圆砾，偶见植物根系，上部一般为混凝土路面，厚约1.2m 粘土2-1（Q3alw2）：褐黄色，硬塑状态，局部呈坚硬状态，裂隙较发育，土质均匀，局部含黑色铁锰质氧化物，切面较光滑。孔隙比平均值0.723，液性指数平均值0.02，压缩系数平均值0.16MPa-1，为中压缩性土。厚2.4m。粉质粘土2-2（Q3alw2）褐黄色，硬塑状态，局部呈坚硬状态，土质均匀，局部含黑色铁锰质氧化物，切面稍具光泽。孔隙比平均值0.635，液性指数平均值-0.01，压缩系数平均值0.17MPa-1，为中压缩性土。厚度3m。粉土1（Q3alw2）：褐黄色，部分地段靠近层底部分呈灰色，稍密，潮湿饱和，摇振反应中等，无光泽反应，干强度低，韧性低，局部夹溥层粉砂，手捏具砂感。厚度3m。圆砾1-1（Q3alw2）：灰色、乳白色、褐黄色等，稍密中密，局部密实，潮湿饱和，以砾石为主，少部分卵石，粒径220mm颗粒平均含量为58.7，粒径大于20mm颗粒平均含量为19.4，最大粒径一般在2040mm，粒间充填中、粗砂为主，不均匀系数Cu平均20.1，属不连续级配，级配良好。磨圆度较好，以次圆状为主，部分滚圆状或次棱角状，成分以石英岩、硅质岩为主。浅黄色、白色等浅色者为石英，褐色、深灰色等为硅质岩，为邕江河流冲积成因。厚度2m。泥岩、粉砂质泥岩1-2（E）：青灰色、灰色，成岩程度较浅，呈坚硬土状，岩芯呈柱状，泥质结构，中厚层状构造，局部含粉砂质，相变为粉砂质泥岩，层理不明显，切面光滑，有腊状光泽。厚度1m。土分层岩土名称天然天然含水量剪切试验压缩模量密度粘聚力内摩擦角wcEs1-2(g/cm3)(%)(kPa)()(MPa)2素填土1.8227.55207.52-1粘土1.9624.71522132-2粉质粘土2.0221.8232412.51粉土2.0219.2161411-1圆砾2.08/030351-2泥岩、粉砂质泥岩2.1813.8101922（3）水文概况场地下水为第四系松散岩类孔隙水，具承压性,主要赋存于圆砾1-1层中，与邕江水位的联系紧密，稳定水位埋深11.5013.20m，渗透系数为100m/d，在设计中取地下水埋深为10.00m 。3、技术要求和工作要求（1）基坑支护设计资料收集： 1）场地岩土工程勘察报告，基坑支护设计参数。 2）建筑红线、施工红线的地形平面图及基础结构设计图；建筑场地及其附近的地下管线、地下埋设物的位置、深度、结构形式及埋设时间等。 3）基坑附近的地面堆载及大型车辆的动、静荷载情况。 4）临近的已有建筑物的位置、层数、高度、结构类型、完好程度。已建时间以及基础类型、埋设深度、主要尺寸、基础距基坑的净距离等。 5）.基坑周围的地面排水情况，地面雨水与污水、上下水管排入和漏入基坑的可能性。 6）已有相似基坑支护的经验性资料。（2）基坑支护方案和降水方案的选择，确定基坑支护围护结构布置，止水、降水技术方案，基坑开挖、监测方案。基坑支护计算断面的确定。（3）按确定的计算断面分别进行基坑支护围护结构、支撑体系设计计算，降水方案计算，基坑稳定性验算，抗隆起验算。（4）要求编写完整的基坑支护设计报告。（5）按照工程设计和施工要求绘制基坑支护设计相关图纸。毕 业 设 计（论 文）任 务 书3对本毕业设计（论文）课题成果的要求包括图表、实物等硬件要求： 一、文字部分：1、设计说明书、结构计算书；2、外文资料翻译（英-汉），设计摘要翻译（汉-英）。二、图纸部分基坑支护设计施工说明、支护结构桩位平面图（含立柱）、支护结构剖面大样图、支撑平面图、立柱桩大样图、管井平面及大样图等。 4主要参考文献： 1 JGJ 120-2012， 建筑基坑支护技术规程 S.2 GB50007-2011，建筑地基基础设计规范 S.3 GB50330-2002 ，建筑边坡工程技术规范S.4 GB50086-2001，锚杆喷射混凝土支护技术规范S.5 CECS22-2005，土层锚杆设计与施工规范 S.6 CECS147-2004，加筋水泥土桩锚支护技术规程S.7 CECS96-97，基坑土钉支护技术规程S.8 徐秀丽.混凝土框架结构设计M，北京：中国建筑工业出版社，2009.9 丰定国.工程结构抗震M，地震出版社，2005.10 候学渊，刘建航.基坑工程手册M.中国建筑工业出版社，1997.毕 业 设 计（论 文）任 务 书5本毕业设计（论文）课题工作进度计划：起讫日期工作内容2015-12-212016-1-12毕业设计任务布置、熟悉工程情况、收集资料，撰写开题报告，翻译专业文献资料。2016-1-132016-3-1收集资料、确定基坑支护设计方案。2016-3-22016-3-12土压力、支护结构、支撑设计计算，midas软件校核手算结果。2016-3-132016-3-31降水方案设计计算。基坑支护设计计算书编写、打印。2016-4-12016-4-10毕业设计期中检查。2016-4-112016-5-3基坑支护平面图、支护结构图纸绘制。基坑支护设计计算书图纸校对、打印，上交毕业设计成果。毕业设计成果包括： 1任务书；2开题报告；4设计报告；5图纸；6专业文献翻译及原文。2016-5-42016-5-12毕业设计报告成文，包括计算书和图纸。2016-5-132016-5-14答辩阶段。所在专业审查意见：通过负责人： 2015 年 12 月21 日 译文题目： Co-Evolution Optimization of Anchored Row Piles for Deep Foundation Pit 原文：Co-Evolution Optimization of Anchored Row Pilesfor Deep Foundation PitAbstract: The thinking of co-evolution is applied to the optimization of retaining and protecting structure for deep foundation excavation, and the system of optimization of anchored row piles for deep foundation pit has been already developed successfully. For the co-evolution algorithm providing an evolutionary mechanism to simulate ever-changing problem space, it is an optimization algorithm that has high performance, especially applying to the optimization of complicated system of retaining and protecting for deep foundation pit. It is shown by many engineering practices that the co-evolution algorithm has obvious optimization effect, so it can be an important method of optimization of retaining and protecting for deep foundation pit. Here the authors discuss the co-evolution model, object function, all kinds of constraint conditions and their disposal methods, and several key techniques of system realization.Key words: genetic algorithm; co-evolution; optimization; anchored row piles; deep foundation pit1 IntroductionIn all kinds of retaining and protecting techniques for deep foundation pit, anchored row piles have been extensively used because of their some features, such as good results, strong adaptability, easy construction and so on. Usually, the design procedures of anchored row piles are: 1) Select preliminarily the types of retaining and protecting piles and the layers of anchor, namely retaining and protecting scheme design; 2) Select preliminarily all members size and material parameters of retaining and protecting structure, namely detailing design; 3) Make calculation and analysis, which includes checking for embedded depth of piles and load capability of anchor, computing internal force of piles and bar arrangement, etc., and adjusting detailing design to meet various demands of the above checking computation; 4) Compare various schemes and find out the scheme whose cost is lowest as the ultimate design of retaining and protecting for deep foundation pit.Generally, designers need to adjust severally and check repeatedly the retaining and protecting scheme and detailing so as to make every computing procedure meet all design demands. However, the design gained from this is only a“ feasible solution” , but not the optimum solution in all the feasible solutions. As we known, every retaining and protecting scheme has many relevant design parameters. Moreover, these design parameters all directly or indirectly affect the investment of engineering. Hence, how to find out a set of optimization parameters to ensure economy and safety is an important problem of the design of anchored row piles, also a complicated optimization problem. For this reason, the authors introduce the genetic algorithm to the optimization of retaining and protecting for deep foundation pit. Studies show that the introduction of genetic algorithm has opened a new path for the optimization of retaining and protecting for deep foundation pit. Here, the authors explore further a co-evolution algorithm that is suitable for the optimization of retaining and protecting for deep foundation pit.2 Model of Optimization of Anchored Row Piles2.1 Anchored row pile system and its optimization objectiveAs a system engineering, the optimization of anchored row piles is a subsystem of the optimization system for deep foundation pit. It can be plot out two hierarchies, scheme optimization and detailing optimization. Retaining and protecting scheme, composed of row pile sub-scheme and anchor sub-scheme, is a certain combination of the types of row piles (bored pile, artificially-excavated pile, pre-cast pile etc.) and the anchor installing (without anchor, one-layer anchor, two-layer anchor and three-layer anchor)(shown in Fig.1). Scheme optimization is to search a combination which meets all kinds of constraint conditions and has the lowest cost at the same time on the given conditions such as engineering information, engineering geological conditions, environmental conditions, construction conditions and so on. The optimization design of detailing structure is, pointing to a certain retaining and protecting scheme, to optimize the detailing structure of piles and anchors and make the detailing structure meet all constrain conditions and the engineering cost minimum. It contains the design of detailing sizes of piles and anchors, the style of bar arrangement, the parameters and quantity of materials, top ring beam, etc. Whether scheme optimization or detailing optimization, their optimization objectives are common, namely making the total engineering cost of anchored row pile system minimum. Its mathematical model is seeking X:where f(X)=object function, namely cost computation function, referring to Chinese flat rate of architectural engineering and architectural engineering unit estimation price list of each province or city;X=a vector which is made up of design variables x1,x2, ,xn. There are only two design variables in scheme optimization, namely the type of row piles(Pt) and anchor installing(Np). And in detailing optimization, there are the following design variables in two aspects: 1) Retaining and protecting pile: pile diameter(H), perimeter-to-perimeter pile spacing (S), embedded depth (hd), concrete grade (Pct), bar arrangement style (Ms), sort of reinforcing steel bar(Pst) etc. 2) Anchor: anchor installing depth (ha), horizontal anchor spacing (Par), inclination angle of anchor(), free anchor length (lf), fixed anchor length (lm), diameter ofthe grouted mass(D), sort of anchor bar(Ast),grade of cement mortar(Cg), etc.s.t.=constrain conditions which must be met, hv(X) is constrain conditions of equations, p is the number of equations, gu(X) is constrain conditions of inequalities, m is the number of inequalities.The above mathematical model of optimization of anchored row piles will have different forms in different design hierarchies or evolutionary spaces.2.2Mathematical model of scheme optimizationAssume that the population of retaining and protecting scheme is A, search the scheme individual a A to make corresponding total engineering cost minimum, namelywhere C=total cost, Ci.si=the cost of the ith sub-scheme of a certain scheme in a scheme space. The retaining and protecting scheme is formed by row pile and anchor sub-schemes, so i equals 1 or 2; feasible = seeking the feasible individual which meets the constrain conditions in scheme population. The objective of scheme optimization is to make the total cost of scheme minimum while it has met the constrain conditions.2. 3 Mathematical model of detailing optimizationThe detailing optimization of anchored row piles is done on the condition that each sub-scheme has been selected. And its mathematical model is the foundation of data structure design.Assume that a certain detailing population (corresponding to a certain scheme) is B, seek the detailing individual b B to make the total cost of design corresponding to B minimum, namelywhereCi.si= the cost of the ith sub-scheme of a certain individual in the detailing space which corresponds to a certain scheme (the ith sub-scheme chooses the sith value available for selection). It is the function of vector Xi.si; Xi.si= Xi.si.1Xisi.2,Xi.si.k, ,Xi.si.l is a vector of design variables of the ith sub-scheme and a piece of detailing chromosomes. Xi.si.k is the kth design variable, and l is the number of design variables; i equals 1 or 2 (the number of sub-scheme is 2). These Xi.si are linked together to form a whole chromosome of a detailing population, namely X1.s1X2.s2. XBi.si.k= the value range (a discrete aggregate) of design variable Xi.si.k.We can know from the formulas (2) and (3) that evolution objectives of both scheme population and detailing population are to search the lowest cost. So a linking, which links two evolution spaces organically, is set up between scheme population and detailing population. Base on this, the fitness of both scheme population individuals and detailing population individuals can be obtained by making the suitable mathematical manipulation to the engineering cost of every individual. And then we will get a unified standard for evaluating individuals.3 Co-Evolution Model and Algorithm3.1 Co-evolution modelIn the optimization design of anchored row piles, scheme design and detailing design are two different design problems that belong to different spaces and levels. The former is problem space, namely scheme space. It is an aggregate of all retaining and protecting schemes. The latter is solution (design) space, namely detailing space. It is an aggregate of all detailing schemes which correspond to each retaining and protecting scheme. They are not only mutual independence but also interrelation and interaction. The optimization design of anchored row piles is the process of alternately searching to scheme space and detailing space. To search scheme space will make retaining and protecting scheme change, which provides the new focus for searching detailing space. Thereby a new detailing space is created. To search detailing space will obtain a detailing solution that meets the demands of retaining and protecting scheme, which affects further searching scheme space and makes the primary retaining and protecting scheme create a new change. To seek further a new detailing solution corresponding to the new retaining and protecting scheme, , keep searching like this until finding a optimum retaining and protecting scheme and a detailing scheme which meet the design demands. The above-mentioned design thinking can be illustrated by problem-space and design-space co-evolution model as shown in Fig.2, where P= scheme space, and S=detailing space.1) There are two distinct search spaces in all searching process, namely scheme space and detailing space.2) Horizontal movement represents an evolutionary process, which is based on the single genetic algorithm (SGA).Scheme space evolves from P(t) to P(t+ 1), P(t+ 2) , and so on;+ Detailing space evolves from S(t) to S(t+ 1) , to S(t+ 2) , and so on, where t,t+ 1,t+ 2, are evolutionary generations.3) Diagonal movement stands for a search process in which goals lead to the solution, namely“ the scheme design leads to detailing design” (downward arrow) and“ the detailing design refocuses scheme design” (upward arrow). The downward arrow: the process from problem to design solution. It is also the process of scheme design leading to detailing design in the optimization of anchored row piles. And it has two guide functions: one is that every individual of scheme population P(t) will generate a new detailing subspace, and provide an object (focus) for this detailing subspace evolution, the other is that every individual of scheme population P(t) will provide the basis of measuring fitness for the population of corresponding detailing subspace. The dashed upward arrow: the process of adjusting problem definition by design. It is also the process of detailing design affecting the scheme design in the optimization of anchored row piles. The effect is realized by sending the evolutionary results of detailing subspace the best detailing solution-to the relevant individual of scheme space and providing the basis of measuring fitness for the scheme individual. It is obvious that in the whole searching process two state spaces interact, and that the evolution of each space is always guided by the most recent population in the other space.3.2 Co-evolution algorithmCorresponding to the above-mentioned co-evolution model, co-evolution algorithm of anchored row piles for deep foundation pit can be described ast:=0;Initialize and generate the scheme population P(t);number:=count(P(t);/determine the size of scheme population while (termination condition of scheme population evolution not satisfied) /while 1I:=0;while (I=number) do/while 2do the following operations to the current individual Pi(t) of scheme population: stochastically create the detailing population Si(t) containing M individuals;execute SGA to the detailing population Si(t), and evolve m generations;if (the feasible solution is found in detailing population) transfer the result of detailing evolution to Pi(t); and measuring fitness of Pi(t); elsegive a little enough fitness to current Pi(t);I: = I+ 1; /end while 2, finish a evolution of detailing subspace Si(t) corresponding/ to scheme individual Pi(t) per loop, and measuring fitness of Pi(t)do statistical analysis to fitness of individuals in scheme population Pi(t);select in scheme population P(t) and create new scheme population P(t+ 1);t: = t+ 1;execute SGA to scheme population P(t+1); /end while 1, the scheme population P(t ) evolves one generation per loopputout the ultimate result of evolution; 4 Several Techniques of System Realization4.1 Structure of fitness functionThe fitness of anchored row piles is a mathematical manipulation of object function, namely engineering cost. It can be defined as followswhere f(X) = object function. In the detailing space, it is equal to the engineering cost of each individual; in the scheme space, it is equal to the engineering cost of the best individual that evolves from the corresponding detailing space.flag= sign of individual feasibility, flag 0,1. If the constraints of design criterion of detailing space are met, the individual is feasible, flag= 1; otherwise, it is unfeasible, flag=0.c=sign of evolution space, c 0,1. c=0 in the scheme space, and c=1 in the detailing space.The meanings of symbols and h(X) refer to the formula (5).4.2 Disposal of constraint conditionsThe genetic algorithm is an optimization method without constraints. To solve optimization problem of anchored row piles, we must convert it into an optimization problem without constraints. So the following methods are adopted in the evolutionary process:The design variable constraints must be met grimly in the two evolutionary spaces, so we mainly adopt three measures. At first, adjust the value range of design variable and try to make the code space be full of data code so as to decrease the number of design variables out of value range. Secondly, for some design variables out of value range in the evolutionary process, adjust them by use of amendment operator. Thirdly, for other design variables out of value range, the genetic operator is invoked to create a new individual randomly by system.The design criterion constraints must be met grimly in the scheme space, otherwise, the relevant detailing evolution will be insignificant. In the detailing space, the penalty function is used to dispose design criterion constraints, namely a problem with constraints is converted into an one without constraints by penalizing unfeasible solutions. The generalized object function is constructed asWhere h(X)= penalty function. The constraints of detailing design criterion are expressed as gi(X)0,i=1,2, ,m. So the penalty function is designed to be h(X) = i=1m| min0,gi(x)|. When an individual meets a certain design criterion constraint, penalty intensity is zero, otherwise, the individual will be penalized, and penalty intensity is defined as“ the absolute value of unsatisfied degree is multi-plied by relevant coefficient”.= penalty factor ( 0). Usually, it increases step by step in the response to evolution. In the initial stage of evolution, the value of is less, and the penalty is gentle. So the livability of unfeasible solutions is biggish, and the excellent genes(traits) of the individual can be hold, which is helpful to enlarge searching space and reach the global best solution. In the late stage of evolution, with the increase of excellent genes (traits), the value of is bigger and bigger, the penalty is more and more powerful. The searching space will be close to the optimum solution. The unfeasible solutions will be bolted quickly, which can avoid the fluctuation of fitness effectively, and accelerate the process of convergence. For example, the value of penalty factor of detailing structure population, which corresponds to the scheme of artificial excavated piles with one layer anchor, is explored from 50 to 1000.4.3 Determination of optimizationEvolutionary system will end when the evolution of scheme space reaches convergence. In other words, if the maximum fitness fmax for several generations in the scheme space does not change or evolutionary generation reaches a maximum value, the calculation will end. By now, the feasible solutions of the scheme and the detailing which correspond to fmax, X* = (Pt* ,Np* ,D* ,S* , )is considered as the optimal design variable vector.5 ConclusionsThe co-evolution algorithm is based on the SGA. As for some design problems in an ever-changing problem space, it provides an evolutionary mechanism to simulate the ever-changing problem space. Therefore, it is an optimization algorithm that has high performance, especially fits to the optimization of retaining and protecting for deep foundation pit. In this paper, a significant attempt has been done to the co-evolution optimization of anchored row piles for deep foundation pit. The engineering practice shows that it has obvious optimization effect and great engineering operation significance and is an important method of the optimization of complicated system of retaining and protecting for deep foundation pit. A future study about the following four aspects must be enhanced: 1) the features of retaining and protecting for deep foundation pit and the reasonable co-evolution algorithm, 2) the structure of fitness function of co-evolution algorithm and the appropriate method of measuring fitness, 3) the system structure of retaining and protecting for deep foundation pit, the hierarchies plotting-out of scheme and detailing, 4) all kinds of constraints of retaining and protecting for deep foundation pit and their disposal methods.中文译文：深基坑桩锚支护协同演化优化设计摘要：将协同演化思想应用于基坑桩锚支护优化设计中，成功开发了深基坑桩锚支护优化设计系统。协同演化方法提供了模拟问题空间不断变化的演化机制，是一种高效的优化算法，适合于深基坑支护这一复杂系统的优化。工程实践表明，该方法具有明显的优化效果，可作为深基坑支护优化设计的一种重要手段。给出了协同演化模型、优化目标函数、全部约束条件及其处理方法以及系统实现的几项关键技术。关键词：遗传算法；协同演化；优化；桩锚支护；深基坑一、前言在各种深基坑围护技术中，桩锚支护结构以其效果好、适应性强和施工简便等特点，在我国得到了广泛应用。桩锚支护的一般设计步骤为：（1）选择支护桩类型和锚杆层数，即支护方案设计；（2）初选支护结构各细部尺寸和材料参数，即细部结构设计；（3）进行计算分析，包括桩的嵌固深度验算、锚杆承载力验算、桩身内力计算、配筋计算等，通过计算对各细部初选参数做出修改和调整，使之满足各种验算要求；（4）对比多个方案，找出造价最低的方案作为基坑支护的最终设计。通常设计者需要对支护方案和细部结构进行多次调整、反复验算，才能使得各计算步骤均满足设计要求。但这样得到的设计往往只是一个“可行”解，而不一定是“最优”解。对于每一种支护方案，其细部设计参数有很多，它们都直接或间接地影响到工程投资。因此，如何寻找一组最佳设计参数，以达到既经济又安全，是桩锚支护设计的一个重要问题。这是一个复杂的优化设计问题，为此，笔者在文献中把遗传算法引入深基坑支护优化设计中来，研究表明，遗传算法的引入为深基坑支护优化设计问题闯出了一条新的途径。然而，由于深基坑支护优化设计一般包括方案优选与细部结构优化两个层次，最初提出的算法比较适用于单层次优化问题，为此，笔者探索了另一种适用于深基坑支护优化设计问题的协同演化算法。二、桩锚支护优化设计模型2.1桩锚支护体系及其优化设计目标桩锚支护优化设计属于一项系统工程，是深基坑支护设计体系中的一个子系统，可以划分为方案优化设计和细部结构优化设计两个层次。支护方案由桩排与锚杆两个子方案构成，是排桩类型（钻孔灌注桩、人工挖孔桩和预制桩等）与锚杆设置（无锚杆即悬臂式、一层锚杆、二层锚杆和三层锚杆）的不同组合形式（图1），方案优化设计就是在给定的工程信息、场地水文工程地质条件、环境条件、施工条件等已知条件下，寻找满足各种约束且造价最低的一种组合；细部结构优化设计则是针对某一确定的支护方案所进行的桩、锚细部结构优化，包括桩、锚的细部结构尺寸、配筋方式、材料参数及材料用量、顶部圈梁的设计等，使得该结构满足各种约束，同时造价最低。方案设计对细部结构设计具有指导作用，细部结构设计结果又可反馈回方案设计中以修改或调整方案设计。无论是方案优化还是细部结构优化，其优化目标是共同的，即桩锚支护体系的总造价最低。其数学模型为：式中f（X）为目标函数，即工程造价计算函数，套用国家统一建筑工程基础定额及各省市建筑工程单位估价表。X是由x1，x2， ，xn组成的向量，是设计过程中要优选的量，即设计变量。在方案设计层次上，其设计变量仅两个，即排桩类型（Pt）与锚杆设置（Np）；在细部结构设计层次上，则包括以下两方面的设计变量：支护桩：桩径（）、桩边距（S）、嵌固深度（hd）、砼强度等级（Pct）、配筋方式（Ms）、钢筋类别（Pst）等；锚杆：锚杆设置深度（ha）、水平间距（PAr）、倾角（）、自由段长度（lf）、锚固段长度（lm）、锚固段直径（D）、锚筋类别（Ast）、水泥砂浆强度等级（Cg）等。s.t.表示需要满足的约束条件，hv（X）为等式约束条件，p为其数目，gu（X）表示不等式约束条件，m表示其数目。上述桩锚支护优化设计数学模型在不同设计层次或演化空间中又有不同的表现形式。2.2方案优化数学模型设支护方案种群空间（染色体空间）为chrom，求方案个体chromchrom，使得chrom对应的方案总造价最小，即式中 Costi。Si表示方案空间中某一方案个体第i个子方案（取第Si个可选值）的造价，由于总的支护方案仅由排桩与锚杆两个子方案构成，因此， i的取值为1和2；feasible表示在方案种群空间中求取满足约束条件的可行个体。方案优化的目标是使方案总造价TotalCost在满足约束条件的情况下取得最小值。2.3细部结构优化数学模型桩锚支护体系的细部结构优化设计是在方案的各子方案选定的条件下进行的，其数学模型是为细部结构优化而进行的数据结构设计的基础。设与某确定方案对应的某细部结构种群空间为xbchrom，求细部结构个体xbchromxbchrom，使得xbchrom对应的设计总造价：式中Costi。Si表示在与某一方案（第i个子方案取第Si个可选值）相对应的细部结构空间中，某一个体的第i个子方案（取第Si个可选值）的造价，它是向量Xi。Si的函数；Xi。Si=Xi。Si。1，Xi。Si。2， ，Xi。Si。k， ，Xi。Si。l为某方案（第i个子方案取第Si个可选值）中第i个子方案所需优化的设计变量向量，是细部结构染色体的一部分， Xi。Si。k为其中的第k个设计变量，l为其设计变量的个数；i取1和2（子方案数为2），将这些Xi。Si连接起来，即X1。S1X2。S2，就构成了某个细部结构种群的整条染色体。XBPari。Si。k为设计变量Xi。Si。k的值域（离散集），它限定了Xi。Si。k的取值范围。由公式（2），（3）可以看出，方案种群和各细部结构种群演化的目标均为寻求最低造价，由此在方案种群和各细部结构种群之间建立起一个纽带，将方案种群的演化和各细部结构种群的演化有机地联系在一起。基于这一点，方案种群个体和各细部结构种群个体的适应值都可通过对造价进行适当的数学变换而得到，从而为评价个体的好坏提供了一个统一的标准。三、协同演化模型及算法3.1协同演化模型在桩锚支护优化设计中，方案设计和细部结构设计是两个不同空间、不同层次的设计问题，前者是问题空间，也叫方案空间，是全体支护方案的集合；后者是解（设计）空间，也叫细部结构空间，是与各支护方案相对应的全体细部结构的集合。这两个空间既相互独立又相互联系、相互影响。桩锚支护优化设计就是对方案空间和细部结
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